1. Field of the Invention
The present invention relates to computer simulation of what are known as giant reservoirs, and more particularly to multi-level solution of large-scale linear systems during simulation of single phase fluid in oil reservoirs and compressible single phase dry gas reservoirs.
2. Description of the Related Art
U.S. Pat. No. 7,526,418, of which Applicant is named as an inventor, and which is of common ownership to the present invention, is a compositional reservoir simulator which performed simulations in shared memory supercomputers, distributed memory supercomputers or clusters of personal computers (PC's) configured as computer data processing units (CPU's). Other reservoir simulation efforts using CPU's are U.S. Pat. Nos. 7,516,056 and 7,684,967.
The linear solution of the pressure equation or temperature equation for the giant systems of equations composed of fine-grid models (seismic-scale 12.5 meter to 25 meter) can represent 50% or more of the total simulation time for reservoir and basin simulations of subsurface geological formations. The linear solver determines the “correction” required for the Newton iteration to converge to the solution of the underlying non-linear system of partial differential equations which define fluid flow, material balance and pressure-volume-temperature conditions of reservoir fluids at a series of time steps. For what are known as giant reservoirs, the number of cells can be millions or even a billion or more. The linear solver process was thus computationally intensive and time consuming.
Even present petascale-capable computing systems, which are systems capable of one quadrillion calculations per second, and are composed of tens of thousands of processors, cannot efficiently solve these systems of equations if inaccurate initial guesses are used for a simulation model which is on a fine grid model. Many expensive linear iterations by the computing systems are wasted in seeking reasonable solution directions based on inaccurate initial guesses.